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Dmitry [639]
1 year ago
5

Jeremy rides his bike at a rate of 15 miles per hour. Below is a table that represents the number of hours and miles Kevin rides

. Assume both bikers ride at a constant rate. Which biker rides at a greater speed? Include all of your calculations in your final answer.
Time in hours (x) Distance in miles (y)
1.5 17.25
2 23
3.5 40.25
4 46
Mathematics
1 answer:
TiliK225 [7]1 year ago
3 0

The correct answer would be, Jeremy rides at a greater speed than Kevin.

Step-by-step explanation:

Jeremy rides at a rate of 15 miles per hour

Kevin rides at a rate given in the table

Let Y be the distance traveled by Jeremy

And X be the number of hours

Then for Jeremy:

y/x = 15/1

=> y= 15 x

For Kevin:  

(46-23)/(4-2)

= 23/2

= 11.5

So for Kevin, Y = 11.5 x

So when Jeremy's and Kevin's rates are compared,

15 > 11.5

which means Jeremy rides at a greater speed.  

Learn more about Time and Distance problem at:

brainly.com/question/3581191

#LearnWithBrainly

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Answer:

a) There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b) There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c) The expected number of Chrome users is 4.074.

d) The variance for the number of Chrome users is 3.2441.

The standard deviation for the number of Chrome users is 1.8011.

Step-by-step explanation:

For each Internet browser user, there are only two possible outcomes. Either they use Chrome, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

Google Chrome has a 20.37% share of the browser market. This means that p = 0.2037

20 Internet users are sampled, so n = 20.

a.Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

This is P(X = 8).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 8) = C_{20,8}.(0.2037)^{8}.(0.7963)^{12} = 0.0243

There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b.Compute the probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

Either there are less than 3 Chrome users, or there are three or more. The sum of the probabilities of these events is decimal 1. So:

P(X < 3) + P(X \geq 3) = 1

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{20,0}.(0.2037)^{0}.(0.7963)^{20} = 0.0105

P(X = 1) = C_{20,1}.(0.2037)^{1}.(0.7963)^{19} = 0.0538

P(X = 2) = C_{20,2}.(0.2037)^{2}.(0.7963)^{18} = 0.1307

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0105 + 0.0538 + 0.1307 = 0.1950

P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1950 = 0.8050

There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c.For the sample of 20 Internet browser users, compute the expected number of Chrome users

We have that, for a binomial experiment:

E(X) = np

So

E(X) = 20*0.2037 = 4.074

The expected number of Chrome users is 4.074.

d.For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

We have that, for a binomial experiment, the variance is

Var(X) = np(1-p)

So

Var(X) = 20*0.2037*(0.7963) = 3.2441

The variance for the number of Chrome users is 3.2441.

The standard deviation is the square root of the variance. So

\sqrt{Var(X)} = \sqrt{3.2441} = 1.8011

The standard deviation for the number of Chrome users is 1.8011.

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